CN105930550A - Method for optimizing boost-skip trajectory of air-breathing hypersonic missile - Google Patents
Method for optimizing boost-skip trajectory of air-breathing hypersonic missile Download PDFInfo
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Abstract
The invention relates to a method for optimizing a boost-skip trajectory of an air-breathing hypersonic missile, and is technically characterized by comprising the steps of designing an air-breathing hypersonic missile trajectory scheme in which a scramjet engine ignites in an intermittent and periodic manner; establishing an air-breathing hypersonic missile longitudinal plane whole trajectory equations of motion including direct force control; and solving the trajectory optimizing problem by using a self-adaptive pseudo-spectral method The optimized boost-skip trajectory significantly improves the range of the missile, with the range being 3.81 times of a boost-cruise trajectory of a conventional air-breathing hypersonic missile; and the designed flight height of the boost-skip trajectory is not fixed and is relatively high at most of the time, a higher penetration capability is gained, and the trajectory mode has very promising prospects.
Description
Technical field
The present invention principally falls into missile trajectory and optimizes field, is specifically related to a kind of air suction type hypersonic missile boosting-jumping
The formula that jumps Method of Trajectory Optimization.
Background technology
Traditional air suction type hypersonic missile from aerial platform launch after, the rocket booster carried by its boosting to facing
Near space height and the flight speed of 4~5Ma, scramjet engine ignition operation subsequently, guided missile flies near space cruise
OK, diving attack is carried out when guided missile is close to target.Cruise section is the stage that whole flight course is the longest, but in cruise
The overload of section guided missile is the least, and maneuverability is extremely limited, and flying height is relative with speed stable, it is likely that captured by air defence system
And interception, limit its penetration ability.And use the air suction type hypersonic missile of direct force gentle Power compound control mode,
Cruise section overload and maneuverability can be improved, by boosting-Jump probability mode, it is possible to dramatically increase the prominent anti-energy of guided missile
Power and range.
Air suction type hypersonic cruise missile boosting-Jump probability optimization problem, different from ballistic missile reentry trajectory,
Air-breathing missile is still the flight course of drive after motors in boost phase penetration terminates, and is affected by scramjet engine duty,
In trajectory optimisation, the restriction to the angle of attack is the strictest, and motor power is along with the value that angle of attack variation is a time-varying, this
Optimization process is needed more join to count to meet the condition of convergence.Additionally, compared with reentry vehicle, existing air suction type
The cruise section overload of hypersonic missile is the least, it is impossible to complete the Jump probability of guided missile, bigger motor-driven for making guided missile have
Ability, needs to use direct force/aerodynamic force complex controll mode, to produce bigger overload, thus necessary in control variable
Comprise precise tracking thrust, further increase the complexity of ballistic design.
Summary of the invention
For the trajectory optimisation problem of air suction type hypersonic missile, the present invention provides a kind of air suction type hypersonic missile
Boosting-Jump probability optimization method, a kind of air suction type hypersonic missile boosting-Jump probability optimization method, described bullet
Road optimization method is for increasing range and the penetration ability of air suction type hypersonic missile, it is characterised in that described trajectory is excellent
Change method designs the air suction type hypersonic missile trajectory of a kind of scramjet engine intermittent cyclical igniting, foundation comprises directly
The air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion of power control and structure one air suction type hypersonic missile
Boosting-Jump probability Optimized model, and described Method of Trajectory Optimization use self adaptation puppet spectrometry solve trajectory optimisation problem.With
Ballistic missile reentry trajectory is different, and air-breathing missile of the present invention is still the flight course of drive after motors in boost phase penetration terminates, by super
The impact of burning ramjet duty, in trajectory optimisation, the restriction to the angle of attack is the strictest, and air suction type of the present invention
The cruise section of hypersonic missile can complete the Jump probability of guided missile, makes guided missile have bigger maneuverability, uses directly
Power/aerodynamic force complex controll mode, produces bigger overload, comprises precise tracking thrust in control variable, the most excellent
Change trajectory.
The present invention is achieved by the following technical solutions:
A kind of air suction type hypersonic missile boosting-Jump probability optimization method, described Method of Trajectory Optimization is used for increasing
Add range and the penetration ability of air suction type hypersonic missile, a kind of scramjet engine of described Method of Trajectory Optimization design
The air suction type hypersonic missile that the air suction type hypersonic missile trajectory of intermittent cyclical igniting, foundation comprise side-jet control is indulged
To the plane overall trajectory equation of motion and structure air suction type hypersonic missile boosting-Jump probability Optimized model and described
Method of Trajectory Optimization uses self adaptation puppet spectrometry to solve trajectory optimisation problem.
Further, the air suction type hypersonic missile trajectory of described scramjet engine intermittent cyclical igniting is basic
Flight scenario is: described hypersonic missile is pushed to 25-60 km height by rocket booster, after rocket booster separates,
First described hypersonic missile experiences unpowered hop segments, when the height of described hypersonic missile be down to below 40 kms,
When speed is down to 1500m/s, scramjet engine ignition operation, described hypersonic missile jumps motor-driven near space,
In Skipping trajectory, scramjet engine uses the mode of intermittent cyclical igniting to work, to reduce the fuel consumption of electromotor
Amount;After running out of gas, described hypersonic missile enters the unpowered jump flight stage, and when near target, described height is ultrasonic
Speed guided missile enters Trajectory-terminal, completes diving attack.
Further, the air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion of side-jet control is comprised described in
Particularly as follows: ignore earth rotation and aspheric impact, it is assumed that precise tracking is provided that continuously adjustabe thrust, obtains described bag
The air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion containing side-jet control is:
In formula, m, v, h, α,θ represents guided missile quality, speed, terrain clearance, the angle of attack, the angle of pitch and trajectory tilt angle respectively;
L is range;P is motor power;FNThrust for precise tracking;nyFor normal g-load;Q is dynamic pressure;S is area of reference;g
For acceleration of gravity;R is earth mean radius;IspFor scramjet engine specific impulse;nyNormal g-load, C can be used for guided missilex,Cy
Being respectively resistance coefficient and lift coefficient, they are the functions of the angle of attack and Mach number.
Further, described air suction type hypersonic missile boosting-Jump probability Optimized model is particularly as follows: become in state
When amount x (t) meets air suction type hypersonic missile boosting-Jump probability constraints, seek optimum control variable u (t), make
Obtain performance indications J minimalization;
Trajectory is divided into motors in boost phase penetration and and jumps by described air suction type hypersonic missile boosting-Jump probability Optimized model
Section is optimized respectively, using motors in boost phase penetration end energy as performance indications J of motors in boost phase penetrationMotors in boost phase penetration,
Using range as performance indications J of hop segmentsHop segments,WhereinFor tfThe scope in moment;
State variable x (t) takes parameter v in the equation of motion, θ, h, L, m, i.e. and x=(v, θ, h, L, m)T;Indulge only considering
In the case of plane motion, control variable is taken as angle of attack and precise tracking thrust FN, i.e. u=(α, FN)T。
Further, described air suction type hypersonic missile boosting-Jump probability constraints includes:
(1) normal g-load constraint
In described motors in boost phase penetration and described hop segments, the overload of guided missile is limited by structural strength and airborne equipment ability to bear
System, i.e. has
|ny|≤ny max (2)
N in formulay maxFor guided missile maximum permissible load factor;
(2) dynamic pressure constraint
Q in formulamaxLimit for guided missile max-Q;
(3) hot-fluid constraint
Hot-fluid constraint is often referred to the hot-fluid at aircraft surface stationary point and limits, and i.e. has
In formulaFor guided missile maximum heat ductility limit system;
Stationary point heat flow density is calculated by following formula:
In formula, kQIt is the constant relevant with missile configuration and material, kQ=3.08 × 10-5;RNFor radius of curvature at stationary point,
Take RN=0.02m;ρ is atmospheric density;V is missile velocity;
(4) angle of attack constraint
Perturb to reduce the separation of two inter-stages, it is necessary to the angle of attack size in restriction booster separation moment:
α(tf1)=0 ° (6)
For meeting the control requirement of guided missile, controlled quentity controlled variable must control within the specific limits, and controlled quentity controlled variable can not acute variation,
On the other hand in hop segments, also restricted to the angle of attack, thus to flight course when Scramjet Inlet normally works
The guided missile angle of attack have a corresponding constraint:
In formula, t01For guided missile x time aloft, tf1For motors in boost phase penetration finish time, t02For punching engine point first
The fire moment, tf2For the moment that runs out of gas, tfFor hop segments finish time;
(5) highly constrained
Reduce flight resistance during for enabling guided missile at high speed flight, avoid the firepower of ground environment to block the most as far as possible
Cut, guided missile should be made to be maintained at the flight of near space region, limit its flying height work is following:
25km≤h≤60km,tf1≤t≤tf (8)
(6) end conswtraint
Air suction type hypersonic missile enters Trajectory-terminal after hop segments terminates, and completes diving attack, for ensureing to dive
Attack and have enough kinetic energy, hop segments trajectory is made following end conswtraint:
H in formulafAnd vfIt is respectively tfThe height of moment guided missile and speed;
(7) precise tracking thrust constraint
Limited by precise tracking quantity and specific impulse, thrust F of precise trackingNHave certain limitations scope
FN≤FN max (10)
In formula, FNFor the thrust of precise tracking, FN maxFor precise tracking maximum thrust;
(8) scramjet engine intermittent cyclical ignition condition
For reducing the Fuel Consumption of scramjet engine, in Skipping trajectory, electromotor uses intermittent cyclical igniting
Mode works, and when experience trough starts to climb, and when flight speed is down to speed of ignition lower limit 1500m/s, ultra-combustion ramjet starts
Machine ignition operation;Rising to 40km, engine misses, guided missile relies on aircraft kinetic energy to continue to climb, and completes several jump ripple
Section, until speed is decreased to speed of ignition lower limit, electromotor is lighted a fire again;And so forth until running out of gas, guided missile enters nothing
Powerhop mission phase;Thus obtaining scramjet engine cycle ignition condition is:
θ≥0°,h≤40km,v≤1500m/s,t02≤t≤tf2 (11)
Further, described employing self adaptation puppet spectrometry solves trajectory optimisation problem and specifically includes following steps:
Step 1: divide network as required interval, and set and count joining of each interval;
Step 2: on each network interval, utilizes overall situation Gauss puppet spectrometry by state equation, object function and constraint
Conditional discrete, is converted into nonlinear programming problem by optimal control problem;
Step 3: utilize sequential quadratic programming method to solve nonlinear programming problem;
Step 4: judge whether quantity of state corresponding to each grid section midpoint and controlled quentity controlled variable meet the pact of the equation of motion
Bundle required precision, requires if met, iteration terminates, if being unsatisfactory for, skips to step 5 or step 6;
Step 5: if the magnitude of all elements is suitable in residual vector β, then increase to join and count, i.e. increase interpolation polynomial
Number of times;
Step 6: if the magnitude of some element is significantly greater than other elements in residual vector β, then to corresponding grid regions
Between refine;
Step 7: after all grid sections have all adjusted, returns step 2, carries out next iteration.
Further, described hypersonic missile is the cruise body with Waverider structure.
The Advantageous Effects of the present invention:
The present invention devises the Air-breathing hypersonic vehicle trajectory of a kind of scramjet engine intermittent cyclical igniting
Scheme, optimizes the boosting-Skipping trajectory obtained and significantly improves the range of guided missile, its flight time 2306.9s, and optimization obtains
Range is 3771.5km, and range is 3.81 times of the boosting-cruise trajectory of existing air suction type hypersonic missile, helping of design
Push away-Skipping trajectory flying height do not fixes, and most of the time flying height is higher, has higher penetration ability, is a kind of
The trajectory mode of great application prospect.
Accompanying drawing explanation
Fig. 1 is boosting of the present invention-jump hypersonic missile basic trajectory schematic diagram;
Fig. 2 is the ballistic curve of difference sparking mode of the present invention;
Fig. 3 is the flight speed change curve of different schemes of the present invention;
Fig. 4 is the vehicle mass change curve of different schemes of the present invention.
Detailed description of the invention
In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, right
The present invention is explained in further detail.Should be appreciated that specific embodiment described herein is used only for explaining the present invention, and
It is not used in the restriction present invention.
On the contrary, the present invention contain any be defined by the claims the replacement done in the spirit and scope of the present invention, repair
Change, equivalent method and scheme.Further, in order to make the public that the present invention to be had a better understanding, thin to the present invention below
During joint describes, detailed describe some specific detail sections.There is no these detail sections for a person skilled in the art
Description can also understand the present invention completely.
Embodiment 1
Carry out trajectory optimisation for the trajectory scheme under different sparking mode, and the performance analyzing different schemes is good and bad.Imitative
True condition is as follows:
State variable initial condition: v0=240m/s, θ0=15 °, h0=15km, L0=0km, m0=1780kg;
End conswtraint: vf>=1200m/s, hf>=30km, mf1=671kg, mf=548kg.
Process constraints: ny max=10, qmax=50kpa,FN max=4000N.
In order to investigate the impact on trajectory of the scramjet engine difference sparking mode, contrast 4 kinds of different trajectory schemes,
The sparking mode of each scheme scramjet engine lists table 1 in.In table 1, the employing intermittent cyclical point that scheme 1 designs for the present invention
The trajectory of fire mode;Scheme 2 uses continuous cycle sparking mode, and the most often one trough guided missile of experience all can be lighted a fire and be climbed;Scheme 3
Middle scramjet engine continuous firing, in the range of therefore its ballistic ordinate is limited in 25~40km;Scheme 4 flies cruise formula for flat
Trajectory, guided missile is not made motor-driven, and engine continuous works, and its level altitude is 35km.
Trajectory scheme under the different sparking mode of table 1
Hp self adaptation puppet spectrometry is utilized respectively the above-mentioned trajectory scheme of air suction type hypersonic missile to be optimized, emulation
As shown in Figure 2 to 4, Fig. 2~Fig. 4 is respectively the different ballistic curve of sparking mode to result, the flight speed of different schemes becomes
Change curve;The vehicle mass change curve of different schemes.
By the simulation result shown in Fig. 2~Fig. 4 it can be seen that in the case of scheme 1, air suction type hypersonic missile passes through
The motors in boost phase penetration of 50s, speed and highly increase respectively to 2118.6m/s and 40km, booster separates subsequently, and guided missile continues to climb
The highest 70km, then starts whereabouts and carries out unpowered jump;Experienced by the jump of 4 wave bands, missile velocity drops to 1500m/
S, scramjet engine starts ignition operation;Scramjet engine is lighted a fire every time and can be made guided missile 2 wave bands of jump, through 4
After secondary igniting, punching engine runs out of gas, and guided missile enters last unpowered glide section;Final missile velocity is down to 1200m/
S, flight time 2306.9s, optimizing the range obtained is 3771.5km.
For scheme 2 scheme, before scramjet engine is lighted a fire, the trajectory of optimization is identical with scheme 1, this rear engine
Often one trough ignition operation of experience, flies to 40km height tail-off, enters unpowered glide through 4 igniting guided missiles
Section;The ballistic range that final optimization pass obtains is 3033.7km, and the flight time is 1762.8s.
Scheme 3 scheme is the Skipping trajectory of scramjet engine continuous firing, the trajectory before engine ignition and scheme 1
Identical, after igniting, guided missile jumps motor-driven in 25-40km altitude range, and the jump post fuel of 2 wave bands of experience exhausts, and punching press is sent out
Motivation is closed, and guided missile enters unpowered hop segments.It is 1912.3km that final optimization pass obtains the range of guided missile, and the flight time is
1089.1s。
In scheme 4 scheme, it is motor-driven that guided missile does not do jump, and its motors in boost phase penetration is high trajectory of throwing, subsequently in 35km height super burn punching
Hydraulic motor ignition operation, guided missile enters to put down and flies cruise section;After running out of gas, guided missile starts to dive downwards, finally gives guided missile
Range be 990km, the flight time is 600s.
Contrasting these 4 kinds of trajectory schemes it can be seen that scheme 1 provides best performance trajectory, its range is existing air suction type
Hypersonic missile is put down and is flown to cruise 3.81 times of trajectory, and the flying height that this trajectory is not fixed, and has higher prominent
Anti-ability.Main reason is that of this advantage, it is leaner that the guided missile most of the time in boosting-Skipping trajectory is positioned at air
Spatial domain, flight kinetic energy rejection is less;On the other hand, scramjet engine uses the mode of intermittent cyclical igniting to work, greatly
Improve greatly the service efficiency of fuel, provide farther range for guided missile.
Claims (7)
1. air suction type hypersonic missile boosting-Jump probability optimization method, described Method of Trajectory Optimization is used for increasing
The range of air suction type hypersonic missile and penetration ability, it is characterised in that a kind of super burn of described Method of Trajectory Optimization design
The air suction type that the air suction type hypersonic missile trajectory of punching engine intermittent cyclical igniting, foundation comprise side-jet control is superb
The velocity of sound guided missile fore-and-aft plane overall trajectory equation of motion and structure air suction type hypersonic missile boosting-Jump probability optimize mould
Type, and described Method of Trajectory Optimization use self adaptation puppet spectrometry solve trajectory optimisation problem.
The most according to claim 1, a kind of air suction type hypersonic missile boosting-Jump probability optimization method, its feature exists
In, the basic flight scenario of the air suction type hypersonic missile trajectory of described scramjet engine intermittent cyclical igniting is: institute
State hypersonic missile and be pushed to 25-60 km height by rocket booster, after rocket booster separates, described hypersonic lead
First bullet experiences unpowered hop segments, when the height of described hypersonic missile be down to below 40 kms, speed is down to 1500m/s
Time, scramjet engine ignition operation, described hypersonic missile jumps motor-driven near space, super burn in Skipping trajectory
Punching engine uses the mode of intermittent cyclical igniting to work, to reduce the Fuel Consumption of electromotor;After running out of gas, described
Hypersonic missile enters the unpowered jump flight stage, and when near target, described hypersonic missile enters Trajectory-terminal,
Complete diving attack.
The most according to claim 1, a kind of air suction type hypersonic missile boosting-Jump probability optimization method, its feature exists
In, described in comprise side-jet control the air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion particularly as follows: ignore ground
Revolutions and aspheric impact, it is assumed that precise tracking is provided that continuously adjustabe thrust, obtain described in comprise side-jet control
The air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion be:
In formula, m, v, h, α,θ represents guided missile quality, speed, terrain clearance, the angle of attack, the angle of pitch and trajectory tilt angle respectively;L is
Range;P is motor power;FNThrust for precise tracking;nyFor normal g-load;Q is dynamic pressure;S is area of reference;G attaches most importance to
Power acceleration;R is earth mean radius;IspFor scramjet engine specific impulse;nyNormal g-load, C can be used for guided missilex,CyRespectively
For resistance coefficient and lift coefficient, they are the functions of the angle of attack and Mach number.
The most according to claim 1, a kind of air suction type hypersonic missile boosting-Jump probability optimization method, its feature exists
In, described air suction type hypersonic missile boosting-Jump probability Optimized model is particularly as follows: meet air-breathing in state variable x (t)
During formula hypersonic missile boosting-Jump probability constraints, seek optimum control variable u (t) so that performance indications J take
Minimum;
Trajectory is divided into motors in boost phase penetration and divides with hop segments by described air suction type hypersonic missile boosting-Jump probability Optimized model
It is not optimized, using motors in boost phase penetration end energy as performance indications J of motors in boost phase penetrationMotors in boost phase penetration,Will
Range is as performance indications J of hop segmentsHop segments,WhereinFor tfThe scope in moment;
State variable x (t) takes parameter v in the equation of motion, θ, h, L, m, i.e. and x=(v, θ, h, L, m)T;Only considering fore-and-aft plane
In the case of motion, control variable is taken as angle of attack and precise tracking thrust FN, i.e. u=(α, FN)T。
The most according to claim 4, a kind of air suction type hypersonic missile boosting-Jump probability optimization method, its feature exists
In, described air suction type hypersonic missile boosting-Jump probability constraints includes:
(1) normal g-load constraint
In described motors in boost phase penetration and described hop segments, the overload of guided missile is limited by structural strength and airborne equipment ability to bear,
I.e. have
|ny|≤ny max (2)
N in formulay maxFor guided missile maximum permissible load factor;
(2) dynamic pressure constraint
Q in formulamaxLimit for guided missile max-Q;
(3) hot-fluid constraint
Hot-fluid constraint is often referred to the hot-fluid at aircraft surface stationary point and limits, and i.e. has
In formulaFor guided missile maximum heat ductility limit system;
Stationary point heat flow density is calculated by following formula:
In formula, kQIt is the constant relevant with missile configuration and material, kQ=3.08 × 10-5;RNFor radius of curvature at stationary point, take RN
=0.02m;ρ is atmospheric density;V is missile velocity;
(4) angle of attack constraint
Perturb to reduce the separation of two inter-stages, it is necessary to the angle of attack size in restriction booster separation moment:
α(tf1)=0 ° (6)
For meeting the control requirement of guided missile, controlled quentity controlled variable must control within the specific limits, and controlled quentity controlled variable can not acute variation, another
Aspect is in hop segments, also restricted to the angle of attack when Scramjet Inlet normally works, and thus leads flight course
Play the angle of attack and have a corresponding constraint:
In formula, t01For guided missile x time aloft, tf1For motors in boost phase penetration finish time, t02When lighting a fire first for punching engine
Carve, tf2For the moment that runs out of gas, tfFor hop segments finish time;
(5) highly constrained
Reduce flight resistance during for enabling guided missile at high speed flight, avoid the firepower of ground environment to intercept the most as far as possible,
Guided missile should be made to be maintained at the flight of near space region, limit its flying height work is following:
25km≤h≤60km,tf1≤t≤tf (8)
(6) end conswtraint
Air suction type hypersonic missile enters Trajectory-terminal after hop segments terminates, and completes diving attack, for ensureing diving attack
There is enough kinetic energy, hop segments trajectory made following end conswtraint:
H in formulafAnd vfIt is respectively tfThe height of moment guided missile and speed;
(7) precise tracking thrust constraint
Limited by precise tracking quantity and specific impulse, thrust F of precise trackingNHave certain limitations scope
FN≤FN max (10)
In formula, FNFor the thrust of precise tracking, FN maxFor precise tracking maximum thrust;
(8) scramjet engine intermittent cyclical ignition condition
For reducing the Fuel Consumption of scramjet engine, in Skipping trajectory, electromotor uses the mode of intermittent cyclical igniting
Work, when experience trough starts to climb, and when flight speed is down to speed of ignition lower limit 1500m/s, scramjet engine point
Firer makees;Rising to 40km, engine misses, guided missile relies on aircraft kinetic energy to continue to climb, and completes several jump wave band, directly
Being decreased to speed of ignition lower limit to speed, electromotor is lighted a fire again;And so forth until running out of gas, guided missile enters unpowered jumping
Jump mission phase;Thus obtaining scramjet engine cycle ignition condition is:
θ≥0°,h≤40km,v≤1500m/s,t02≤t≤tf2 (11)
The most according to claim 1, a kind of air suction type hypersonic missile boosting-Jump probability optimization method, its feature exists
Solve trajectory optimisation problem in, described employing self adaptation puppet spectrometry and specifically include following steps:
Step 1: divide network as required interval, and set and count joining of each interval;
Step 2: on each network interval, utilizes overall situation Gauss puppet spectrometry by state equation, object function and constraints
Discretization, is converted into nonlinear programming problem by optimal control problem;
Step 3: utilize sequential quadratic programming method to solve nonlinear programming problem;
Step 4: judge whether quantity of state corresponding to each grid section midpoint and controlled quentity controlled variable meet the constraint essence of the equation of motion
Degree requirement, requires if met, iteration terminates, if being unsatisfactory for, skips to step 5 or step 6;
Step 5: if the magnitude of all elements is suitable in residual vector β, then increase to join and count, i.e. increase the secondary of interpolation polynomial
Number;
Step 6: if the magnitude of some element is significantly greater than other elements in residual vector β, then corresponding grid section is entered
Row refinement;
Step 7: after all grid sections have all adjusted, returns step 2, carries out next iteration.
The most according to claim 1, a kind of air suction type hypersonic missile boosting-Jump probability optimization method, its feature exists
In, described hypersonic missile is the cruise body with Waverider structure.
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